Comment = Critique + Request
"Comments" are a service provided by the Stack Exchange Network to quickly say what was wrong with a post, what could be improved, request something missing. In any case a comment should be directly related to the post it is posted on. We all know that far too many comments go beyond this. And we probably tolerate too many of them.
Criteria for comment moderation were put in these words recently:
Except here. We do moderate comments, ruthlessly! Which frequently leads to a fair bit of culture-shock from folks who are used to the meaning of "comment" everywhere else on The Internet.
Here, comments really are considered to be not much more than clutter once they are resolved. Even if issues were not resolved a comment is of little use later because it obviously did not reach what it was intended for.
Taking this radical view we should claim to delete all comments after a while, best being done automatically by a robot to avoid bad feelings for a person (aka moderator) who manually pulled the delete trigger.
Now we do not have such a radical view here, as can be seen from many comments that just stay.
Comments can be so confusing
But it may help to understand why we do not really want to be bothered long with reading through lengthy comment threads in case a flag was raised for comment deletion. Actually we still do, but the more confusing such a comment thread became the less likely it will help any future visitor and then it should be deleted all together.
We want our users to write clear and interesting questions, which will lead to great answers covering all aspects of a question. This should leave as little room as possible for additional information given in comments.
We know that many users still prefer to write a short comment rather than a long answer. In the long run, and from the view of an external visitors, this is bad for the site. We still do not delete such a useful comment. But we will if the information of that comment found its way into an answer. The comment then became obsolete.
Ideally, whenever we write an answer to a question we should take care to also include all useful information given in comments to then flag this comment as obsolete. This can also be done in an edit.
Comment is not Chat
Very long still ongoing comment "discussions" will be moved to chat, the place they belong.
Comments are inspiring
It is great if a comment raised a new question. That is German Language SE at its best! We should then ask this new question, linking to that question in the comment thread but then we should delete all comments about this new question to lead people to the right place, and to stop ongoing discussions which likely are off topic to the other question but very much welcome at the new question.
Please avoid linking to comments in questions or answers as these links may no longer exist after a comment clean-up.
Meta issues should not be discussed on a post but in a Meta question and answer instead. As you may have noticed, here on Meta comments have a different function. They help to resolve issue with the site, and they will not confuse new visitors looking for answers on the German language. On Meta we only rarely will delete a comment, and if so mostly because of a rude flag they may have caught.
No fun allowed?
Sometimes a comment is useless but it is hilarious. This may be an unofficial reason why a comment stays. We also come here for having fun, don't we?
There are no fixed criteria for comment moderation other than comments being not really important.